10th International Society for Music Information Retrieval Conference (ISMIR 2009)CONTINUOUS PLSI AND SMOOTHING TECHNIQUESFOR HYBRID MUSIC RECOMMENDATION
Kazuyoshi Yoshii
Masataka Goto
National Institute of Advanced Industrial Science and Technology (AIST){k.yoshii,m.goto}@aist.go.jp

ABSTRACT

Rating dataaFeaturesabb

Features3 likesbzcFeatures9 likescc

Recommender12

3
Topic 2

Topic 1a

Example of recommendation
Features
The objective is to recommendzz
who likes
Train continuous-pLSI model items to
c

b

c

…

…

This paper presents an extended probabilistic latent semantic indexing (pLSI) for hybrid music recommendation that
deals with rating data provided by users and with contentbased data extracted from audio signals. The original pLSI
can be applied to collaborative filtering by treating users
and items as discrete random variables that follow multinomial distributions. In hybrid recommendation, it is necessary to deal with musical contents that are usually represented as continuous vectorial values. To do this, we propose a continuous pLSI that incorporates Gaussian mixture models. This extension, however, causes a severe local optima problem because it increases the number of parameters drastically. This is considered to be a major factor generating “hubs,” which are items that are inappropriately recommended to almost all users. To solve this problem, we tested three smoothing techniques: multinomial
smoothing, Gaussian parameter tying, and artist-based item
clustering. The experimental results revealed that although
the first method improved nothing, the others significantly
improved the recommendation accuracy and reduced thehubness. This indicates that it is important to appropriately
limit the model complexity to use the pLSI in practical.

Content-based data

1 likes
2 likes…

…

9

Topic 3 … Topic 5…

Estimation of musical tastes
is likely to select Topic 3zz is recommended to

Figure 1. Hybrid recommender based on continuous pLSI.
passive experience in which users only receive “default”
recommendations into an interactive experience in whichusers can freely customize (personalize) those recommendations. To achieve this, it is necessary to let users clearly
understand and express their own musical tastes that are estimated as bases of making default recommendations. The
conventional reasoning like “You like A, so you would likeB because other users who like like A also like B” is a relative expression of musical tastes. We aim to obtain a direct
expression of each user’s musical tastes that is easy to use
as a basis for interactive recommendation.
A promising way to do this is to use probabilistic latentsemantic indexing (pLSI) based on a multi-topic model,
which has been originally used for document modeling [1].
The model includes latent variables corresponding to theconcepts of topics. How likely a document and a word cooccur is predicted by stochastically associating each document and word with a topic. Documents and words that arestrongly associated with the same topic are likely to occur
jointly. The model can be applied to collaborative filtering
based on rating histories by treating documents and words
as users and items [2]. Given a user, we can predict how
likely each item is purchased by estimating how likely theuser chooses each topic. The musical tastes of users can be
expressed as the strength of user-topic associations.
As shown in Figure 1, we propose continuous pLSI forhybrid recommendation that enhances serendipity by combining rating data with content-based data extracted frommusical audio signals. Specifically, Gaussian mixture models (GMMs) are built into the collaborative filtering modelof pLSI in order to address continuous vectorial data. Unlike the major collaborative methods relying on heuristics[3,4], the pLSI model can be extended in a consistent manner because it is flexible and has a theoretical basis.

1. INTRODUCTION
The musical tastes of users of online music distribution services that provide millions of items are strongly influenced
by the characteristics of the music automatically recommended by those services. Users often have difficulty retrieving unknown items they might like. In such case, users
consider recommendations and get aware of what kinds ofitems are their favorites. When only popular items are always recommended, users are not exposed to items theymight enjoy more and get used to enjoying only the “safe”
recommendations. This in turn strengthens the tendency torecommend only popular items. In other words, there is asevere limitation in serendipity of music discovery. In fact,
this negative-feedback phenomenon has been observed inmany services based on collaborative filtering.
We aim to enhance the serendipity by transforming thePermission to make digital or hard copies of all or part of this work forpersonal or classroom use is granted without fee provided that copies are
not made or distributed for profit or commercial advantage and that copies
bear this notice and the full citation on the first page.
c 2009 International Society for Music Information Retrieval.
339

Oral Session 4: Music Recommendation and Playlist Generation
et al. [14] discussed content-based recommendation basedon the Earth-Movers distance between GMMs of individual items. They empirically found that a homogenization
method can improve performance [15]. Hoffman et al. [16]tried to solve this problem by using the hierarchical Dirichlet process (HDP) for modeling content-based data. Unlike
the GMM, the HDP represents each item as a mixture ofan unfixed number of Gaussians. The number is automatically adjusted to match the data complexity. In addition,
the same set of Gaussians is used to model all items, with
only the mixture weights varying from item to item. Thisis similar to Gaussian parameter tying.

The continuous pLSI, however, suffers from a serious
local optima problem because a number of parameters linearly increases according to data size. This causes the hub
phenomenon [5], in which specific items are almost always
recommended to users regardless of their rating histories.
Thus, the serendipity of recommendations is insufficient.
Although a similar probabilistic model was proposed forgenre classification [6], this problem was not addressed.
To solve this problem, we propose three smoothing techniques: multinomial smoothing, Gaussian parameter tying,
and artist-based item clustering. The first technique is expected to avoid overfitting and the other two reduce themodel complexity. We compared the effectiveness of thesetechniques experimentally.
The rest of this paper is organized as follows. Section 2
introduces related work. Section 3 explains a model of thecontinuous pLSI. Section 4 describes the three smoothing
techniques. Section 5 reports our experiments. Section 6summarizes the key findings of this paper.

3. CONTINUOUS PLSIThis section explains a continuous pLSI model and a training method suitable for efficient parallel processing.
3.1 Problem Statement
We define several symbols from a probabilistic viewpoint.
Let U = {u1 , u2 , · · · , u|U| } be the set of all users, where|U | is the number of them, and let V = {v1 , v2 , · · · , v|V | }be the set of all items, where |V | is the number of them. Letu and v be discrete random variables respectively taking
the values of one member of U and one member of V . Let
X = {x1 , x2 , · · · , x|V | } denote content-based data thatis a set of D-dimensional feature vectors extracted fromindividual items. Let x be a continuous random variablein the D-dimensional space. Probabilistic distributions are
represented as p(variable) or p(variable1|variable2), e.g., adiscrete distribution p(u) or a conditional continuous distribution p(x|u). For example, probabilities or probability
densities are given by p(u = ui ) or p(x = xj |u = ui ),which are simply described as p(ui ) or p(xj |ui ).
As to available rating data, we mainly assume implicit
ratings such as purchase histories or listening counts, which
are recorded automatically even when users do not explicitly express their preferences for individual items. In general, the number of implicit ratings tends to be much larger
than that of explicit ratings. We thus think that the former
are more suitable to probabilistic approaches because forthem the sparseness problem is less serious.
The total available data (combinations of rating data andcontent-based data) is given by O = {(u(1) , v(1) , x(1) ),· · · , (u(N ) , v(N ) , x(N ) )}, where (u(n) , v(n) , x(n) ) (1 ≤ n≤ N ) is a user-item-feature co-occurrence that user u(n)has purchased (viewed or listened to) item v(n) with feature x(n) and N is the number of co-occurrences. Letc(u, v) be the number of times that 
co-occurrence (u, v, x)
was observed. Obviously, N =u,v c(u, v). An easy
way to utilize explicit ratings (e.g., numerical rating scoressuch as the numbers of “stars” in an one-to-five scale rating system adopted by Amazon.com) is to set the value ofc(u, v) to one if a user u likes item v, i.e., the rating scoreis greater than a neutral score (three stars). Alternatively,
we could use rating scores for weighting c(u, v).
The final objective is to estimate the probabilistic distribution p(v|u), which indicates how likely it is that user u
likes item v. Recommendations are then made by ranking
items not rated by user u in a descending order of p(v|u).

2. RELATED WORKMusic recommendation is an important topic today in thefield of music information processing. Conventional studies on recommendation have been intended to deal with
textual data (documents and words). In addition, many researchers have proposed various ideas to make the mostof content-based data that is automatically extracted frommusical audio signals. For example, Logan [7] proposed acontent-based recommender based on the cosine distance
between a user’s favorite items and non-rated items. Magnoand Sable [8] reported subjective experiments showing thata content-based recommender competes against Last.fm (acollaborative recommender) and Pandora (a recommender
based on manual annotations) in terms of user satisfaction.
These reports indicate the synergistic effect of integrating
rating data with content-based data. Hybrid recommenders
have been actively investigated recently. Celma et al. [9]used both content-based similarity and user profiles given
in RSS feeds to choose suitable items. Tiemann et al. [10]integrated two weak learners (social and content-based recommenders) by using an ensemble learning method.
Another important issue is how to present recommendations to users. Donaldson and Knopke [11] visualized therelationships of recommended items in a two dimensional
space. Lamere and Maillet [12] proposed a transparent andsteerable interface for a recommender based on crowds ofsocial tags. A common concept of these studies seems tobe that users had better actively explore or control recommendations. This would result in enhanced serendipity.
The existence of hubs has recently been recognized asa serious problem. Interestingly, this problem was not reported in the field of text-based recommendation. In music
recommendation and retrieval, GMMs are generally used
to represent the distributions of acoustic features. Aucouturier et al. [5] pointed out that this kind of modeling tends
to create hubs that are wrongly evaluated as similar to allother items. Berenzweig [13] concluded that the hub phenomenon is related to the curse of dimensionality. Chordia

340

10th International Society for Music Information Retrieval Conference (ISMIR 2009)u

3.2 Model Formulation
The graphical representation of a continuous pLSI modelis shown in Figure 2. This is an extended version of threeway aspect models [17, 18] in which all variables are discrete. We assume that users, items, and features are conditionally independent through latent topics. In other words,
once a latent topic is specified, there is no mutual information between three kinds of variables. Although this seems
a strong assumption, it is a reasonable way to avoid the local optima problem. Introducing a dependency edge fromitems to features in order to model the real world accurately
would increase the number of parameters drastically.
The pLSI model can explain the process generating cooccurrence (u(n) , v(n) , x(n) ). Let Z = {z1 , · · · , z|Z| } bea set of topics, where |Z| is the number of them. Let z be alatent variable that takes the value of one of Z. Each topic
can be regarded as a soft cluster that is simultaneously associated with users and items. That is, each user and each
item stochastically belong to one of the topics. The model
thus treats triplet (u(n) , v(n) , x(n) ) as incomplete data thatis latently associated with z(n) ∈ Z. The complete data isgiven by quartet (u(n) , v(n) , x(n) , z(n) ). An interpretationof the generative process is that user u(n) stochastically selects topic z(n) according to his or her taste p(z(n) |u(n) ),and z(n) stochastically generates item v and its features x
in turn. For convenience, we let S be {z(1) , · · · , z(n) }.
A unique feature of the continuous pLSI is that p(x|z)
is modeled with a Gaussian mixture model (GMM) in order to deal with continuous observation x. Let M be thenumber of mixtures (Gaussian components). Each topic
zk ∈ Z has a GMM defined by the mixing proportionsof Gaussians {wk,1 , · · · , wk,M } and their means and covariances {μk,1 , · · · , μk,M } and {Σk,1 , · · · , Σk,M }. As
in the original pLSI, p(u), p(z|u), and p(v|z) are multinomial distributions. We practically use an equivalent definition of the model obtained by focusing on p(z), p(u|z),
and p(v|z). The parameters of these multinomial distributions are simply given by (conditional) probability tablesof target variables. Let θ be the set of all parameters of |Z|
GMMs and |Z|(1 + |U | + |V |) multinomial distributions.

v

=

u,v

Q(θ|θcurrent ) = ES [log p(S, O)]c(u, v)p(z|u, v, x) log p(u, v, x, z),

z

Topic

p( x | z )Gaussian mixture modelx

Item(discrete)

Feature(continuous)

Figure 2. Graphical representation of continuous pLSI.
where p(z|u, v, x) is a posterior distribution of latent variable z and can be calculated by using the current parameters θcurrent as follows:p(u, v, x, z)p(z|u, v, x) = .
z p(u, v, x, z)(4)

In the M-step we update the current parameters by maximizing Eqn. (3). Note that log p(u, v, x, z) can be decomposed into log p(z) + log p(u|z) + log p(v|z) + log p(x|z).
This means that the parameters of each distribution can be
updated independently. To update p(z), for example, weonly focus on a term related to p(z) as follows:
Qp(z) =c(u, v)p(z|u, v, x) log p(z). (5)u,vzUsing a Lagrange multiplier λ for a constraint of probability standardization, we define a new function Fp(z) asp(z) .
(6)
Fp(z) = Qp(z) + λ 1 −z

We then calculate the differential of Eqn. (6) with respect
to p(z) and set it to zero as follows:∂Fp(z)1 =c(u, v)p(z|u, v, x) − λ ≡ 0. (7)∂p(z)p(z) u,v
The updated distribution p(z) can be obtained byu,v c(u, v)p(z|u, v, x)p(z) = .
u,v,z c(u, v)p(z|u, v, x)(8)The other two multinomial distributions p(u|z) and p(v|z)
can be similarly updated as follows:c(u, v)p(z|u, v, x)p(u|z) =  v,(9)u,v c(u, v)p(z|u, v, x)u c(u, v)p(z|u, v, x).
(10)p(v|z) =u,v c(u, v)p(z|u, v, x)
To update continuous distribution p(x|z), we focus on
Qp(x|z) =c(u, v)p(z|u, v, x) log p(x|z) (11)(1)

This can be easily calculated for given observations whenparameters θ are obtained.
In the E-step we define a Q function asMultinomial

Multinomial

3.3 Model Training
The training method we explain here uses the ExpectationMaximization (EM) algorithm [19] and is a natural extension of previous methods [17, 18] (c.f., discrete HMM v.s.
continuous HMM). Instead of maximizing the incomplete
log-likelihood, log p(O), the EM algorithm maximizes the
expected complete log-likelihood ES [log p(S, O)] iteratively, where Ez [f (z)] means an expected value of function f (z) with respect to p(z); Ez [f (z)] = z p(z)f (z).
The complete likelihood of (u, v, x, z) is given byp(u, v, x, z) = p(z)p(u|z)p(v|z)p(x|z).

p (u | z )User’s tastep (v | z )User(discrete)

u,v

=

(2)


u,v

(3)

c(u, v)K
k=1

p(zk |·) logzMp(yk,m )p(x|zk , yk,m ), (12)m=1where to improve legibility we wrote p(z|u, v, x) as p(z|·).

z

341

Oral Session 4: Music Recommendation and Playlist Generationyk ∈ {yk,1 , · · · , yk,M } is a latent variable that indicates
which Gaussian in the GMM of topic zk generates x. p(yk )represents a probability distribution over M Gaussians, i.e.,p(yk,m ) = wk,m , and p(x|zk , yk,m ) is the likelihood thatfeature x is generated from a Gaussian indicated by yk,m .
Because the logarithmic operation for the summation makes
Eqn. (12) hard to maximize directly, we focus on the expected value of Qp(x|z) with respect to yk :Eyk [Qp(x|z) ] =Mc(u, v)

u,v



K


This can be separately calculated in each machine. To calculate p(z|u, v, x), we need only p(z), p(u|z) (u ∈ Ui ),p(v|z) (v ∈ Vj ), and p(x|z). The number of parameters ofthese distributions is much smaller than the total numberof parameters. Finally, we can get an integrated result byp(z) ∝
cz (Ui , Vj ).
(20)
1≤i≤GU ,1≤j≤GV

p(zk |·)

k=1

4. SMOOTHING TECHNIQUES

To avoid overfitting, one needs to use appropriate smoothing techniques. In our study, we use three techniques to improve accuracy and reduce hubness: multinomial smoothing, Gaussian parameter tying, and artist-based item clustering. The first relaxes the excessive inclination of multinomial parameters, and the others limit model complexity.

p(yk,m |x, zk ) log wk,m + log N (x|µk,m , Σk,m ) , (13)m=1where p(yk,m |x, zk ) is a posterior probability given byp(yk,m )p(x|zk , yk,m )p(yk,m |x, zk ) = M.
m=1 p(yk,m )p(x|zk , yk,m )(14)

To obtain optimized wk,m , we define the following function by introducing a Lagrange multiplier β:MFwk = Eyk [Qp(x|z) ] + β 1 −wk,m .
(15)

4.1 Multinomial Smoothing
We add a conjugate prior called a Dirichlet distribution toa Q function as a regularization term. To estimate p(z), forexample, we consider the following function:

m=1

Qp(z) = Qp(z) + Dir(α),

Calculating the partial partial differential of Eqn. (15) withrespect to wk,m and setting it to zero, we obtain

where α is a set of K parameters of a Dirichlet distribution.
This results in the additive smoothing method. We set allparameters to 1.0001. Maximizing Qp(z) , we getu,v c(u, v)p(zk |·)p(yk,m |x, zk )wk,m = Mm=1u,v c(u, v)p(zk |·)p(yk,m |x, zk )

.

(16)



u,v c(u, v)p(z|u, v, x) + α − 1p(z) =  

Setting the partial differential of Eqn. (13) to zero, the mean
and variance μk,m and Σk,m are obtained by

u,vµk,m = Σk,m =c(u, v)p(zk |·)p(yk,m |x, zk )xu,v c(u, v)p(zk |·)p(yk,m |x, zk )

u,v c(u, v)p(zk |·)p(yk,m |x, zk )(x − µk,m )

u,v c(u, v)p(zk |·)p(yk,m |x, zk )

(21)

.
c(u,
v)p(z|u,
v,
x)
+
α
−
1
u,v

z

(22)

The updating formulas of the other multinomial distributions are similarly given by, (17)

v c(u, v)p(z|u, v, x) + α − 1,p(u|z) =  uv c(u, v)p(z|u, v, x) + α − 1u c(u, v)p(z|u, v, x) + α − 1.
p(v|z) =  v
u c(u, v)p(z|u, v, x) + α − 12. (18)

Given a user u
i , recommendations are made by evaluating p(v|ui ) = z p(v|z)p(z|ui ), where p(z|ui ) is proportional to p(z)p(ui |z) and indicates the musical tastes ofuser u: how likely it is user ui selects (likes) topic z.

(23)
(24)

4.2 Gaussian Parameter Tying
We force all GMMs to share the same set of Gaussians anddiffer from each other in the mixing proportions of those
Gaussians. In the context of HMMs, this is called a tied
mixture model. The new updating formulas are given by

3.4 MapReducing EM Algorithm
Computational efficiency, a very important issue in music recommendation when the database and model becomelarge, is especially critical when used data cannot be loadedon the memory of a single machine. Elegant implementations, however, have scarcely been addressed.
A remarkable advantage of pLSI-based recommenders
is that we can easily implement them in parallel processing environments that consist of multiple machines suchas clusters. Google News, for example, uses a distributed
computation framework called MapReduce [20].
We can implement the continuous pLSI by using MPI or
Hadoop [21]. Suppose we have GU GV machines (CPUs).
Let {U1 , · · · , UGU } and {V1 , · · · , VGV } be exclusive setsof users and items, where U1 ∩ · · · ∩ UGU = U and V1 ∩· · · ∩ VGV = V . To update p(z), for example, we calculatecz (Ui , Vj ) =c(u, v)p(z|u, v, x).
(19)


u,v,m
µk,m = u,v,m c(u, v)p(zk |·)p(yk,m |x, zk )Σk,m =c(u, v)p(zk |·)p(yk,m |x, zk )xu,v,m c(u, v)p(zk |·)p(yk,m |x, zk )(x − µk,m )u,v,m c(u, v)p(zk |·)p(yk,m |x, zk ), (25)

2. (26)

4.3 Artist-based Item Clustering
We replace item-based distribution p(v|z) with artist-based
distribution p(a|z), where variable a represents one of theartists in the database. Let A be a set of items sung by artista, That is, let all items be grouped according to their artist
names. We train an artist-based model for users, artists,and features by iteratively updating p(a|z) as follows:u,v∈A c(u, v)p(z|u, v, x)p(a|z) = .
(27)u,v c(u, v)p(z|u, v, x)u∈Ui ,v∈Vj342

10th International Society for Music Information Retrieval Conference (ISMIR 2009)
Score
Counts
Ratio

5
5336
68.5%

4
1458
18.7%

3
457
5.86%

2
211
2.71%

1
333
4.27%

Disabled
SM3

Table 1. Distribution of rating scores.

SM1
4.29
6.72

SM2
6.18
19.4

SM1&2
6.57
19.3

Table 2. Expected utility of recommendations: Higherscores indicate better performance.

To recommend items rather than artists, we then construct an item-based model by replacing p(a|z) with p(v|z).
To do this, we use an incremental training method [18] thatre-estimates a distribution of unknown items p(v|z) without affecting other trained distributions p(z), p(u|z),(x|z):

Disabled
SM3

Disabled
5.94
5.98

SM1
5.81
5.81

SM2
6.39
6.36

SM1&2
6.36
6.34

Table 3. Entropy of recommendations: Higher scores indicate better performance (fewer hubs).

p(z)p(u|z)p(x|z)
u c(u, v) z p(z)p(u|z)p(x|z)
p(v|z) = .
p(z)p(u|z)p(x|z)
u,v c(u, v) z p(z)p(u|z)p(x|z)

Disabled
4.65
7.10

(28)
ing, Gaussian parameter tying, and item clustering are respectively called SM1, SM2, and SM3. The number oflatent variables was 256 (|Z| = 256). Although the number of mixtures was 32, when SM1 was disabled it was set
to 1 in order to avoid overfitting.
We conducted 10-fold cross validation by splitting thepositive explicit ratings into ten groups. Nine groups wereused for making recommendations with the eight models.
The other group was considered to be not observed andwas used for evaluating the recommendations.

5. EVALUATION
We experimentally evaluated the continuous pLSI in termsof accuracy and hubness by using various combinations of
the smoothing techniques.
5.1 Data
The music items we used were Japanese songs recorded insingle CDs that were ranked in weekly top-20 sales rankings from Apr. 2000 to Dec. 2005. To use these items,
we need real implicit ratings c(u, v) such as purchase histories and listening counts, but most online services do
not release such data to the public. We therefore insteadcollected explicit ratings (numbers of “stars” ranging from
one to five) from Amazon.co.jp by using official APIs [22]that let us download almost all the information available
from Amazon.co.jp [22]. For reliable evaluation, we excluded users who had rated fewer than two items and excluded items that had been rated less than two times. As
a result, |U | was 1872 and |V | was 1400. The number ofartists was 471. If a rating score given to item vj by user ui
was greater than three (the neutral score), we set c(ui , vj )to the score. Otherwise, we set c(ui , vj ) to zero. In otherwords, we considered only positive ratings. A similar approach has been used previously [23]. Note that, as shownin Table 1, the distribution of rating scores was strongly
skewed. The density of 6794 positive ratings (scores 4 and
5) was 0.259% in the user-item co-occurrence table.
With regard to the content-based data, we focused on
vocal features because all the items included singing voicesthat strongly affected the musical tastes of users. To extract
these features from polyphonic audio signals, we used amethod proposed by Fujihara et al. [24]. We calculated a
13-dimensional feature vector at each frame where singing
voices were highly likely to be included, concatenated themean and variance of the feature vectors in each item into a
26-dimensional vector, and then used principal component
analysis to compress the dimensionality to 20 (D = 20).

5.3 Measures
Recommendation results given as ranked lists of items were
evaluated in terms of accuracy and hubness.
To calculate accuracy, we used the expected utility of aranked list [25], which for each user is defined as|V |−#(rated items)

Ru =


r=1

max(scoreu,r − 3, 0),2(r−1)/(γ−1)(29)

where scoreu,r is the rating score that user u actually gave
the r-th ranked item although the item was considered a
non-rated item (the score was hidden) in model training.
When scoreu,r was not available, its value was set to 3.
γ is a viewing half-life based on the assumption that theprobability that a user views an r-th ranked item is twice
the probability that the user views an (r + γ)-th ranked
item. We set γ to 5 as in the literature [25]. Ru was notsensitive to the value of γ. The total score is given byRu
R = 100  u max (0 ≤ R ≤ 100),
(30)
R
u u
where Rumax is the maximum achievable utility if all itemswith available scores given by user u had been at the top of
the ranked list in order of those scores. Basically, higher
values indicate better performance, but note that the probability of recommending known items is high.
We propose the following hubness measure based theentropy of recommendations:


|V |

t(j)
t(j)
H =−
log
,
(31)
|U |
|U |
j=1

5.2 Protocols

where t(j) is the number of times that item vj was recommended with the highest (top 1) ranking. A larger H(higher entropy) indicates a smaller bias in how many times
each item is recommended.

To test all combinations of the three smoothing techniques,
we prepared eight models of the continuous pLSI. For convenience, throughout Section 5, the multinomial smooth-343

Oral Session 4: Music Recommendation and Playlist Generation
5.4 Results
As shown in Table 2, the accuracies of recommendations
were greatly improved by using SM3. This can be explained from two aspects: the relationship between items
and features and that between items and users. First, theitems of each artist tend to be similar to each other in theirmusical features. Second, most users of Amazon.co.jp tend
to like any of the items of the few artists they like. This
would be a common tendency of the users of many online
music distribution services. Therefore, SM3 reduced thecomplexity of the model while preserving almost all theinformation of the rating data.
SM2 improved the accuracy of recommendations maderegardless of the combinations in which it was used. Interestingly, recommendations obtained by jointly using SM2
and SM3 were much more accurate than those made whenthese techniques were used independently. SM1, on theother hand, slightly reduced the accuracy because it is basedon additive smoothing. It is known that its approximation
errors are larger than those of the other smoothing methods
such as the Good-turing method.
Table 3 shows hubness of recommendations. SM2 significantly reduced the hubness while the SM1 and SM3
had no gains. This is consistent with the results reportedby Hoffman et al. [16], who found that HDP and vector
quantization (VQ) did not produce many hubs. VQ can beconsidered as a hard clustering version of the tied GMM,
which is a soft clustering model.
We conclude that combining SM2 and SM3 is the best
approach to improving performance. In our experiments,
it yielded accuracy comparable with that of conventional
methods of collaborative filtering.
6. CONCLUSION
This paper has presented a continuous-pLSI-based modelfor hybrid music recommendation. The model uses GMMs
to represent distributions of acoustic features extracted frommusical audio signals. As in the original pLSI, users anditems are assumed to follow multinomial distributions. We
developed an algorithm for parameter estimation and implemented it in a parallel processing environment. Experimentally testing the abilities of three smoothing techniques—multinomial smoothing, Gaussian parameter tying, andartist-based item clustering—, we found that using the second and third techniques to adjust model complexity significantly improved the accuracy of recommendations andthat the second technique could also reduce hubness.
In the future, we plan to introduce conjugate priors of all
distributions (GMMs and multinomial distributions) into
the continuous pLSI to enable full Bayesian estimation.
Extending latent Dirichlet allocation (LDA) [23] and HDPLDA [26] are worth considering.
Acknowledgement: This study was partially supported by
Grant-in-Aid for Young Scientists (Start-up) 20800084.

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